Nato air strikes are said to have killed 25 Afghans including many civilians, hours after US troops were urged to avoid hurting non-combatants.
The Nato-led Isaf force said it regretted the "apparent" loss of life in Nangarhar province, where its forces had been conducting operations.
It said it would work with an inquiry ordered by President Hamid Karzai.
Gen David Petraeus, in a directive issued on Wednesday, emphasised the need to avoid civilian casualties.
"Every Afghan civilian death diminishes our cause," he said.
'Flood victim funeral'
Mohammad Hassan, head of Nangarhar's Khogyani district, told news agencies that between 12 and 14 people had been killed in one incident.
Villagers were carrying the body of a flood victim for burial in their home village when they were bombed by Nato planes, he told the Reuters news agency.
The attack was also reported by the Pakistan-based Afghan Islamic Press news agency.
It quoted local people as saying that a passenger vehicle carrying the body from Nangarhar's provincial capital Jalalabad to the Hesarak Ghaljai area had stopped near the River Hashimkhel because of a rise in the water level.
It was bombed as it stopped on the main road, the agency said.
An Associated Press cameraman filmed freshly dug graves in a cemetery said to contain victims of the air strike.
AP also filmed bomb damage in the neighbouring district of Sherzad, where village elder Rahmatullah Sherzad told the agency that 13 people had been killed.
Abdul Qadir, described as a relative of one of the victims, said: "If these infidels and crazies are not going to leave our country, we are going to attack Jalalabad City and then there will not be any governor or Karzai."
Mohammad Hassan told AFP he had information that 14 people were killed in the second incident, in which several houses were bombed.
"It's not clear how many of them are civilians or Taliban," he said. "There are some civilians among them."
Mr Karzai's office said the Afghan leader was "saddened by the reports of civilian casualties in Khogyani", and had instructed the authorities to investigate the incident "immediately and thoroughly".
Rear Admiral Greg Smith, Isaf director of communication, said: "Coalition forces deeply regret that our joint operation appears to have resulted in civilian loss of life and we express our sincerest condolences to the families.
"We will partner with the government of Afghanistan to conduct a thorough investigation of this incident, and to provide solatia [compensation] to the families of the civilians killed during the engagement."
Isaf said Afghan and coalition ground forces had "conducted operations in multiple locations" in Nangarhar province on Wednesday, but it talked only of Sherzad district.
While searching for a Taliban commander at a compound, troops came under attack and returned fire, killing "several insurgents", it said.
As the soldiers were leaving the area, they came under new attack, and "an air weapons team provided cover fire", Isaf added.
Voice of Jihad, an Afghan Taliban website, said US airborne forces had launched a raid on Khogyani at 0130 on Thursday (2100 GMT Wednesday), killing eight Taliban fighters.
According to the Taliban source, seven civilians were killed in air strikes during the fighting and a further 10 civilians died when they were bombed from the air "while removing the bodies of the martyrs".